Inequalities among higher-order difference sets, or, remarks on a construction of Ruzsa

Abstract

Extending a little-known construction of Ruzsa, we characterize the quadruples $(s,t,u,v)$ of nonnegative integers such that the inequality $|sA-tA|\le |uA-vA|$ holds for all finite sets $A\subseteq \mathbb{Z}$